The U.S. surgeon general warns that Omicron has not yet peaked.

Dr. Vivek Murthy, the U.S. surgeon general, warned on Sunday that the Omicron surge of coronavirus cases had not yet peaked nationally, saying that the next few weeks would be very difficult in many parts of the country as hospitalizations and deaths rise.

In an interview on CNN’s “State of the Union,” Dr. Murthy noted the “good news” of the plateaus and drops in known cases in the Northeast, especially in New York City and New Jersey.

But “the challenge is that the entire country is not moving at the same pace,” he said, adding “we shouldn’t expect a national peak in the coming days.”

“The next few weeks will be tough,” he said.

The highly contagious Omicron variant has fueled an explosive surge of known cases, with an average of more than 800,000 new cases a day reported on Saturday, according to a New York Times database.

Dr. Ashish Jha, dean of the Brown University School of Public Health, also expressed concerns that the next several weeks would overwhelm hospitals and staff. “Right now we’re at about 150,000 people in the hospital with Covid,” he said on “Fox News Sunday.” “That’s more than we’ve ever had. I expect those numbers to get substantially higher.”

In addition, Omicron has brought into sharp relief the longstanding lack of adequate testing supplies, with consumers now depleting pharmacies of costly rapid tests — a boxed set of two tests ranges from $14 to $24 — and creating long lines at testing sites.

The federal government has promised to distribute one billion rapid at-home coronavirus tests to Americans, limiting each household to request four free tests. And new federal rules require private insurers to cover up to eight at-home tests per member a month.

But with the test orders and reimbursement processes hampered by delays, Americans will likely not have tests in hand for weeks, which may be too late in some places where demand is high as infections spread.

“We’ve ordered too few testing kits, so our testing capacity has continued to lag behind each wave,” Tom Bossert, the homeland security adviser to President Trump, said on ABC’s “This Week.” “It’s too little and too late, but noteworthy for the next wave.”

While many people infected with Omicron have had no or mild symptoms, others — especially those who were not vaccinated and those with chronic conditions — suffered more serious illnesses that were already overwhelming hospitals in some states late last year.

Dr. Murthy disagreed with the Supreme Court’s decision last week that rejected President Biden’s vaccine-or-testing mandate for large employers that would have applied to more than 80 million workers.

“Well, the news about the workplace requirement being blocked was very disappointing,” Dr. Murthy said. “It was a setback for public health. Because what these requirements ultimately are helpful for is not just protecting the community at large; but making our workplaces safer for workers as well as for customers.”

Nearly 63 percent of the U.S. population is fully vaccinated, but only 38 percent of those have received a booster shot, which some have argued should be the new definition of full vaccination. The Centers for Disease Control and Prevention has not changed the definition of full vaccination, but said recently it considers three doses of Pfizer-BioNTech or Moderna’s vaccines to be “up-to-date,” as well as Johnson & Johnson’s shots with a second dose, preferably of Moderna or Pfizer-BioNTech.

Last week, the C.D.C. finally acknowledged that cloth masks do not offer as much protection as a surgical mask or respirator, which some experts have urged the agency to recommend for the general public.

“Please, please get vaccinated,” Dr. Murthy said on ABC, issuing a reminder that the shots still provide good protection against severe illness. “It’s still not too late.”